Geodesic equations and algebro-geometric methods

For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," Prague, 2012. Relativity and Gravitation, volume 157 of Springer Proceedings in Physics, p 91. Springer International Publishing, 201

Functional morphology and efficiency of the antenna cleaner in Camponotus rufifemur ants

Contamination of body surfaces can negatively affect many physiological functions. Insects have evolved different adaptations for removing contamination, including surfaces that allow passive self-cleaning and structures for active cleaning. Here, we study the function of the antenna cleaner in Camponotus rufifemur ants, a clamp-like structure consisting of a notch on the basitarsus facing a spur on the tibia, both bearing cuticular ’combs’ and ’brushes’. The ants clamp one antenna tightly between notch and spur, pull it through, and subsequently clean the antenna cleaner itself with the mouthparts. We simulated cleaning strokes by moving notch or spur over antennae contaminated with fluorescent particles. The notch removed particles more efficiently than the spur, but both components eliminated >60% of the particles with the first stroke. Ablation of bristles, brush and comb strongly reduced the efficiency, indicating that they are essential for cleaning. To study how comb and brush remove particles of different sizes, we contaminated antennae of living ants, and anaesthetized them immediately after they had performed the first cleaning stroke. Different sized beads were trapped in distinct zones of the notch, consistent with the gap widths between cuticular outgrowths. This suggests that the antenna cleaner operates like a series of sieves that remove the largest objects first, followed by smaller ones, down to the smallest particles that get caught by adhesion.To AH: Research grant from the Konrad-Adenauer-Foundation To DL: Research grant from the Cusanuswerk To WF: UK Biotechnology and Biological Sciences Research Council (BB/I008667/1)This is the final version of the article. It first appeared from RSC via http://dx.doi.org/10.1098/rsos.15012

Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with the Reissner-Nordstr\"om space-time.Comment: 22 pages, 14 figures, accepted for publication in PR

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic Kleinian sigma functions restricted to the one-dimensional theta-divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.Comment: 18 pages, 11 figure

Cognitive change predicts symptom reduction with cognitive therapy for posttraumatic stress disorder

Objective: There is a growing body of evidence for the effectiveness of trauma-focused cognitive behavior therapy (TF-CBT) for posttraumatic stress disorder (PTSD), but few studies to date have investigated the mechanisms by which TF-CBT leads to therapeutic change. Models of PTSD suggest that a core treatment mechanism is the change in dysfunctional appraisals of the trauma and its aftermath. If this is the case, then changes in appraisals should predict a change in symptoms. The present study investigated whether cognitive change precedes symptom change in Cognitive Therapy for PTSD, a version of TF-CBT. Method: The study analyzed weekly cognitive and symptom measures from 268 PTSD patients who received a course of Cognitive Therapy for PTSD, using bivariate latent growth modeling. Results: Results showed that (a) dysfunctional trauma-related appraisals and PTSD symptoms both decreased significantly over the course of treatment, (b) changes in appraisals and symptoms were correlated, and (c) weekly change in appraisals significantly predicted subsequent reduction in symptom scores (both corrected for the general decrease over the course of therapy). Changes in PTSD symptom severity did not predict subsequent changes in appraisals. Conclusions: The study provided preliminary evidence for the temporal precedence of a reduction in negative trauma-related appraisals in symptom reduction during trauma-focused CBT for PTSD. This supports the role of change in appraisals as an active therapeutic mechanism

Age-related glomerulosclerosis and interstitial fibrosis in Milan normotensive rats: A podocyte disease

Age-related glomerulosclerosis and interstitial fibrosis in Milan normotensive rats: A podocyte disease. In Milan normotensive (MNS) rats glomerulosclerosis and interstitial fibrosis develop spontaneously in the absence of hypertension. Renal changes were sequentially assessed in these rats between 2 and 10 months of age. At 10 months, rats were characterized by heavy proteinuria, increased serum creatinine, focal or global glomerulosclerosis in 51 ± 12% of the glomeruli as well as tubulointerstitial injury involving > 25% of the section area. Cell injury in podocytes (evidenced as increased expression of desmin and by electron microscopy) and interstitial fibroblasts (increased expression of α-smooth muscle actin) and mild glomerular hypertrophy were witnessed as early as three to four months of age and preceded glomerulosclerosis and interstitial fibrosis. Only minor evidence of mesangial cell activation (as assessed by glomerular de novo α-smooth muscle actin or type I collagen expression or increased cell proliferation) was noted throughout the observation period. Later stages of the disease were characterized by glomerular and/or tubulointerstitial macrophage influx and osteopontin expression (a chemoattractant), mild accumulation of lymphocytes, platelets, fibrinogen, as well as by a progressive accumulation of various matrix proteins. Progressive renal disease in MNS rats is thus noteworthy for the relative lack of mesangial cell activation. Rather, early podocyte damage, induced by yet unknown mechanisms, may underlie the development of glomerulosclerosis and subsequent interstitial fibrosis